论文标题
无序点原子云上连续指标的多项式时间算法
Polynomial-time algorithms for continuous metrics on atomic clouds of unordered points
论文作者
论文摘要
分子的最基本模型是无序原子云，即使没有化学键可以取决于距离和角度的阈值。原子云之间最强的等效性是刚性运动，这是翻译和旋转的组成。实验和模拟分子的现有数据集需要在距离度量方面连续量化相似性。虽然M有序点的云通过Lagrange的二次形式（距离矩阵或革兰氏矩阵）连续分类，但由于M的指数数，它们的扩展为无序点是不切实际的！排列。我们提出的新指标在固定维度n的任何欧几里得空间中的无序点的数字m中都可以在多项式时间内进行计算。
The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a composition of translations and rotations. The existing datasets of experimental and simulated molecules require a continuous quantification of similarity in terms of a distance metric. While clouds of m ordered points were continuously classified by Lagrange's quadratic forms (distance matrices or Gram matrices), their extensions to m unordered points are impractical due to the exponential number of m! permutations. We propose new metrics that are continuous in general position and are computable in a polynomial time in the number m of unordered points in any Euclidean space of a fixed dimension n.
